Coriolis mass flowmeter-densimeters are preferably used for measuring a mass flow rate and/or a density of a fluid flowing through a pipe with a high degree of accuracy.
A flexural mode Coriolis mass flowmeter-densimeter, as is well known, is a vibration meter that has at least one fluid-conducting flow tube which is inserted into a pipe in a fluid-tight manner, particularly in a pressure-tight manner, and which during operation oscillates multimodally, particularly bimodally, about a position of rest at at least one frequency. By means of an electromechanical excitation arrangement, the flow tube is commonly excited in a first, flexural mode of vibration such that Coriolis forces are produced in the moving fluid. In the case of a straight flow tube, the first, flexural mode may, for instance, be a fundamental mode of an elastic beam clamped at both ends, which, as is well known, has a single antinode. In the case of a bent flow tube, particularly a U- or Ω-shaped tube, a fundamental mode of a beam clamped at one end is usually excited as the first, flexural mode.
In such vibration meters, the Coriolis forces caused in the moving fluid by the first, flexural mode simultaneously excite a second vibration mode, whose amplitude is also dependent on mass flow rate.
To determine the mass flow rate, a vibration of the flow tube at an inlet end and a vibration of the flow tube at an outlet end are sensed by means of a suitable sensor arrangement and converted into a first sensor signal, representing the inlet-side vibrations, and a second sensor signal, representing the outlet-side vibrations.
Since the second vibration mode, here also a flexural mode, is superimposed on the first flexural mode, the two vibrations differ in phase. In Coriolis mass flowmeter-densimeters, this phase difference, which is also measurable between the two sensor signals in a corresponding manner, serves as a measurand representative of mass flow rate.
In Coriolis mass flowmeter-densimeters, a resonance frequency and/or the amplitude of the first, flexural mode are generally measurably dependent on the density of the fluid. Thus, if the flow tube is constantly excited at the resonance frequency of the first, flexural mode, for example, this resonance frequency is a measure of the instantaneous density of the fluid.
Vibration meters of the kind described, particularly Coriolis mass flowmeter-densimeters, have been known for a long time. For example, U.S. Pat. Nos. 4,187,721, 4,801,897, 4,876,879, 5,301,557, 5,357,811, 5,557,973 5,648,616, 5,687,100, 5,796,011, and 6,006,609 as well as European Patent 866 319 each disclose a vibration meter for measuring a mass flow rate and a density of a fluid flowing through a pipe, which vibration meter comprises:                a transducer assembly                    with at least one flow tube inserted into the pipe,                            which is clamped at an inlet end and an outlet end so as to be capable of vibratory motion, and                which in operation oscillates relative to a position of rest at an adjustable excitation frequency,                                    with an electromechanical excitation arrangement for simultaneously producing spatial deflections and elastic deformations of the flow tube, and            with a sensor arrangement, responsive to lateral deflections of the flow tube,                            for generating a first sensor signal, representative of an inlet-side deflection of the flow tube, and                for generating a second sensor signal, representative of an outlet-side deflection of the flow tube; and                                                meter electronics                    with an excitation circuit which generates an excitation current for feeding the excitation arrangement, and            with an evaluating circuit which derives from the first and second sensor signals a mass flow rate value representative of the mass flow rate of the fluid and a density value representative of the density of the fluid.                        
Another physical parameter that is important for describing a moving fluid is viscosity. One can distinguish between kinematic viscosity and dynamic viscosity.
Viscometers and density-measuring vibration meters for moving fluids are also known in the art. U.S. Pat. No. 4,524,610, for example, discloses a vibration meter for measuring a viscosity of a fluid flowing through a pipe, which vibration meter comprises:                a transducer assembly                    with a straight flow tube inserted into the pipe which                            has a lumen conducting the fluid and                is clamped at an inlet end and an outlet end so as to be capable of vibratory motion,                                    with an electromechanical excitation arrangement for producing lateral deflections and/or torsional vibrations of the flow tube, and            with a sensor arrangement, responsive to torsional vibrations of the flow tube, for generating a sensor signal representative of central torsions of the flow tube; and                        meter electronics                    with an excitation circuit which generates an excitation current feeding the excitation arrangement, and            with an evaluating circuit                            which derives from the sensor signal and the excitation current a viscosity value representative of the viscosity of the fluid.                                                
In this vibration meter serving as a viscometer-densimeter, the flow tube oscillates either alternately in the above-mentioned first, flexural mode for determining density or in a torsional mode for determining viscosity, or in both modes simultaneously, but at different frequencies. The torsional vibrations performed by the flow tube cause shearing forces in the fluid, which, in turn, have a damping effect on the torsional vibrations.
WO-A 95/16897 discloses a radial mode vibration meter serving as a Coriolis mass flowmeter-densimeter-viscometer for measuring a viscosity of a fluid flowing through a pipe, which vibration meter comprises:                a transducer assembly                    with a straight flow tube inserted into the pipe, which flow tube                            has a lumen conducting the fluid and                is clamped at an inlet end and an outlet end so as to be capable of vibratory motion,                                    with an electromechanical excitation arrangement for producing axisymmetric deformations and/or lateral deflections of the flow tube, and            with a sensor arrangement, responsive to axisymmetric deformations of the flow tube, for producing a sensor signal representative of the deformations of the flow tube; and                        meter electronics                    with an excitation circuit which generates an excitation current feeding the excitation arrangement, and            with an evaluating circuit                            which derives from the sensor signal and the excitation current a viscosity value representative of the viscosity of the fluid.                                                
In this Coriolis mass flowmeter-densimeter-viscometer, the flow tube for determining viscosity and mass flow rate oscillates primarily in an axisymmetric radial mode, i.e., in a mode in which the wall of the flow tube is elastically deformed in such a way that an axis of gravity of the flow tube remains essentially in a static position of rest. In addition, the flow tube is exited, at least temporarily, in a secondary mode for instance in the before mentioned first, flexural mode, which serves to determine the density and pressure of the fluid.
While WO-A 95/16897 describes that radial mode vibration meters can be used to measure both the mass flow rate and the viscosity of fluids, the use of such vibration meters for mass flow rate measurements has so far been limited nearly exclusively to gaseous fluids. It has turned out that the damping effect of viscosity, particularly on the amplitude of the above-mentioned, preferably mass-flow-rate-dependent second vibration mode, is so high that even at viscosities that are just slightly above that of water, this second vibration mode is practically no longer detectable with sensors.
U.S. Pat. No. 5,359,881 discloses a method of measuring the viscosity of a moving fluid which uses a flexural mode Coriolis mass flowmeter-densimeter to determine mass flow rate and in which a pressure difference in the moving fluid along the direction of flow is additionally sensed to determine the viscosity of the fluid.
Furthermore, U.S. Pat. Nos. 5,253,533 and 6,006,609 disclose flexural mode Coriolis mass flow/density sensors which, in addition to sensing mass flow rate and/or density, are suited for determining the viscosity of a fluid. These Coriolis mass flow/density sensors each have a straight flow tube which in operation oscillates, simultaneously with a first, flexural mode, in a torsional mode and thereby performs, at least in sections, torsional vibrations about a longitudinal axis of the flow tube.
It has turned out that the viscosities hitherto determined in such Coriolis mass flow meters by measuring solely the excitation current practically only for the purpose of compensating the primary measured values, namely a mass flow rate value and a density value, are too inaccurate to be suitable for output as additional viscosity values.